A least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition

Qiaolin He*, Roland GLOWINSKI, Xiao Ping Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this article, we discuss a least-squares/fictitious domain method for incompressible viscous flow around obstacles with Navier slip boundary condition. Assuming that Ω and B are two bounded sub-domains of Rd, with B‾⊂Ω, in order to solve the incompressible Navier–Stokes equations with a Navier slip condition on the boundary γ of the obstacle B, we advocate a fictitious domain method where one solves a simpler variant of the original problem on the whole Ω, followed by a well-chosen correction over B. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. A detailed discussion of the finite element implementation of the above methodology is also provided. Numerical results are given; they suggest optimal order of convergence.

Original languageEnglish
Pages (from-to)281-297
Number of pages17
JournalJournal of Computational Physics
Volume366
DOIs
Publication statusPublished - 1 Aug 2018

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Fictitious domain method
  • Incompressible viscous flow
  • Least-squares
  • Navier slip boundary condition

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